2018 : Simulating the Final Ladder After Round 4

Time to dust off the code that simulates the remainder of the home and away season to see, at this very early stage, how it assesses the teams are faring.

METHODOLOGY

Again this year, projections for the remaining games will be made using the MoSHBODS System.

Probability estimates will be derived using MoSHBODS' opinions in the following way:

• Teams' offensive and defensive ratings as at the end of the most-recently completed round will be used, along with the most-recent Venue Performance Values, to calculate expected scores for both the Home and the Away team in every remaining game of the home and away season.
• In that calculation for each contest, both teams' offensive and defensive ratings will be perturbed by a random amount based on drawing from a Normal distribution with mean 0 and standard deviation of 24. The value of 24 was determined by analysing the probability scores produced had the methodology been used to estimate finals chances in previous seasons, starting the simulations from different points in those seasons. The value of 24, while not optimal for every starting point, did well generally (and Occam's Razor and all that nudges us towards preferring a single value for all starting points) 
• These expected scores will be converted into expected Scoring Shots using the average Scoring Shot conversion rate for all teams from 2017 (about 53%). If, when we make the random perturbations for a game, either team is then expected to register fewer than 10 Scoring Shots, their expectation is set to exactly 10 Scoring Shots
• In turn, these expected Scoring Shots values will be used to simulate the outcome of each remaining game in the season, using a model similar to the one derived in this 2014 blog, which comprises a random draw for each team first for Scoring Shots and then for a Conversion rate.

In this latest set of simulations, the entire remaining season was simulated 50,000 times.

RESULTS

The table below should be fairly self-explanatory and it feels a little early to be making any meaningful comments about trends, so for this week I'll provide it without commentary.

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GAME IMPORTANCE

This year, as I did last year, I'm going to use the results of the simulations to estimate the importance of each of the remaining games to the finals chances of every team. For this purpose I'll be first using a measure that I now know was proposed by Mark F Schilling and which defines the importance of game G to a team T as the change in that team's chances of achieving some goal  - here, making the finals - if the Home team wins that game compared to if the Home team loses. (I'll be ignoring draws in this calculation).

To estimate this for a particular game and team using the simulation results we simply look at how often that team made the finals in all the simulation replicates where the Home team won the game being analysed, and compare this to how often it made the finals when the Home team lost that game.

The differences is those percentages are what's shown in the middle portion of the table below (which can be clicked on to access a larger version).

Shown here are the 30 games estimated as likely to have the greatest impact on the composition of the finalists.

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It shows, for example, that Essendon's estimated chances of making the finals differ by about 14% points depending on whether they win or lose their Round 9 clash with the Cats (in which, Essendon are the Home team).

We can see that games generally have most impact on the finals chances of the teams directly involved in them, but that there can also be secondary effects for other teams expected to be in the race for finals spots. For example, for that same game, Adelaide and Port Adelaide's chances improve by about 1% if Essendon prevail instead of Geelong.

It's important not to read too much into small differences in any of the percentages shown here. We are still very early in the season, so there are a lot of probabilities being multiplied in estimating teams' finals chances, each containing its own uncertainty and potential bias.

On the far right of the table is the Weighted Average Importance figure, which is the basis on which the 30 games shown here were determined and which is calculated for any game as follows:

1. Calculate the probability-weighted absolute change in a team's chances of making the final 8 across the three possible outcomes, Home win, Draw, Home loss. So, for example, if a team were a 27% chance of making the finals if the Home team won, a 26% chance if they drew, and a 22% chance if the Home team lost, and if the probabilities of those three outcomes were 70%, 1% and 29%, respectively, the calculation would be:
   70% x abs(27% - 25.5%) + 1% x abs(26% - 25.5%) + 29% x abs(22% - 25.5%) = 2.1%
   
   The 25.5% used in the calculation is the team's unconditional probability of making the finals, and the final number can be thought of as the expected absolute change in the team's finals chances after the result of this particular game is completed.
    
2. Form a simple average of these expected absolute changes.

This final figure can be thought of as the average amount by which teams' finals chances will alter on the basis of the result of this game. Note that, in contrast to the 2015 methodology, I now form this average including all teams. That means there will be some teams whose contribution to the average is zero or nearly zero because their chances of making the finals are close to 0 or 1 regardless of the outcome of the game.

Small differences in the Weighted Average Importance figures for different games should also be treated with caution at this stage and larger differences paid more heed.

We'll get a much clearer picture of which games are most likely to influence the finals makeup as the season progresses.